Update July 2019
The phrase "5 number summaries" has been replaced with "summary statistics" because NZ grapher lists more than this in the graph section. But we are mainly concerned with 5 of them, min, lq, median, uq and max.
SPORT SCIENCE
Austrialian Athletes - Comparing female and male weights
PROBLEM
I wonder if the median weights of Australian male athletes tend to be larger than the median weights of female athletes from the NZGrapher Sport Science survey. From my own observations and general knowledge I think the male athletes will weigh more.
PLAN
I have been given a random sample of data from NZGrapher. The sample size is 100 females and 102 male athletes. Using NZGrapher I will create a dot and box plot with summary statistics so I can analyse and make a conclusion about which gender of athlete weighs more.
DATA
Comparing Medians
The median weight for Australian male athletes is 83 kg and for female athletes 68.05 kg. This is a difference of 14.95 kg. This indicates that the males tend to weigh more than the female athletes. Based on this sample I would expect similar results back in the population of Australian athletes, that male athletes tend to be heavier than female athletes.
Comparing Distributions (spread)
For the spread, the male IQR (middle 50%) is slightly larger at 16.5 kg (90.3-73.8 kg) compared to the female athletes middle 50% of 14.4 kg (74.45 - 60.05 kg), a difference of 2.1 kg. This means there is a bit more variation in the weights of male athletes than female athletes.
Shift
Looking at the graphs I see that the middle 50% of the male box (73.8kg - 90.3kg) is shifted to the right of the female box (60.05kg - 74.45kg) about a 14 kg difference. Again ths suggests that the male athletes tend to be taller than female athletes back in the population of Australian athletes.
Shape
In terms of shape of the graphs, the male dot plot is almost bell shape or symmetrical, slightly skewed to the right (positive skewing) caused by 2 or 3 athletes in the 110 to 120 kg range. The female dot plot shows more of a bell shape though slight skewing to the left (negative skewing) caused by a number of athletes in the 73 - 74 kg range.
Overlap
There is a slight overlap of the boxes, where the females UQ is slight higher than the males' LQ (74.45 - 73.8 kg). This means that a some female athletes are similar in weight to the male athletes.
So far the data indicates that there is a considerable difference between the two groups of athletes. The data is telling me that male athletes are likely to be heavier than female athletes back in the population of Australian athletes.
Conclusion:
From my investigation I can conclude from this sample that the median weight of Australian male athletes tends to be greater than female athletes back in the Australian athlete population with medians of 83 kg and 68.05 kg respectively. I can make this call because, (referring to the graph) the median weight for the male athletes is outside the box (middle 50%) of female athletes.
The value of the DBM/OVS ratio is 14.95/30.25 = 0.49. and since this is greater than 1/3 I can make the call that the Australian male athletes tend to be on average heavier than female athletes. I expect that this result would be reflected in the real Australian athlete population. . This is confirmed by the median values in the summary statistics above. The median weight for the males is 83kg and the median weight for females is 68.05 is 92kg.
The sample size of 100 and 102 samples from each group is usually regarded as sufficient to provide reliable data to answer the investigative question. However, a larger sample size will always provide a more accurate estimate of the true population of Australian athletes. The slight difference in numbers is unlikely to affect the validity of the investigation. If I was to take another sample I would expect to achieve similar results but not identical box plots and summary statistics.
This investigation revolved around the issue of athletic sports. Different types of athletic sports suit different body types and weights. Long distance runners can be very different in weight than athletes involved in weight lifting, discus and shot put. We don't know the individual sports that these athletes belonged to. Perhaps a better comparison would have been made if athletes were sampled from one sport, such as runners with runners, weight lifters with weight lifters etc.
However, I believe from the results of this investigation show that Australian male athletes tend to be heavier than female athletes back in the Australian athlete population. This makes sense as other studies I have carried out show that males also tend to be taller than females in the population.
The median weight for Australian male athletes is 83 kg and for female athletes 68.05 kg. This is a difference of 14.95 kg. This indicates that the males tend to weigh more than the female athletes. Based on this sample I would expect similar results back in the population of Australian athletes, that male athletes tend to be heavier than female athletes.
Comparing Distributions (spread)
For the spread, the male IQR (middle 50%) is slightly larger at 16.5 kg (90.3-73.8 kg) compared to the female athletes middle 50% of 14.4 kg (74.45 - 60.05 kg), a difference of 2.1 kg. This means there is a bit more variation in the weights of male athletes than female athletes.
Shift
Looking at the graphs I see that the middle 50% of the male box (73.8kg - 90.3kg) is shifted to the right of the female box (60.05kg - 74.45kg) about a 14 kg difference. Again ths suggests that the male athletes tend to be taller than female athletes back in the population of Australian athletes.
Shape
In terms of shape of the graphs, the male dot plot is almost bell shape or symmetrical, slightly skewed to the right (positive skewing) caused by 2 or 3 athletes in the 110 to 120 kg range. The female dot plot shows more of a bell shape though slight skewing to the left (negative skewing) caused by a number of athletes in the 73 - 74 kg range.
Overlap
There is a slight overlap of the boxes, where the females UQ is slight higher than the males' LQ (74.45 - 73.8 kg). This means that a some female athletes are similar in weight to the male athletes.
So far the data indicates that there is a considerable difference between the two groups of athletes. The data is telling me that male athletes are likely to be heavier than female athletes back in the population of Australian athletes.
Conclusion:
From my investigation I can conclude from this sample that the median weight of Australian male athletes tends to be greater than female athletes back in the Australian athlete population with medians of 83 kg and 68.05 kg respectively. I can make this call because, (referring to the graph) the median weight for the male athletes is outside the box (middle 50%) of female athletes.
The value of the DBM/OVS ratio is 14.95/30.25 = 0.49. and since this is greater than 1/3 I can make the call that the Australian male athletes tend to be on average heavier than female athletes. I expect that this result would be reflected in the real Australian athlete population. . This is confirmed by the median values in the summary statistics above. The median weight for the males is 83kg and the median weight for females is 68.05 is 92kg.
The sample size of 100 and 102 samples from each group is usually regarded as sufficient to provide reliable data to answer the investigative question. However, a larger sample size will always provide a more accurate estimate of the true population of Australian athletes. The slight difference in numbers is unlikely to affect the validity of the investigation. If I was to take another sample I would expect to achieve similar results but not identical box plots and summary statistics.
This investigation revolved around the issue of athletic sports. Different types of athletic sports suit different body types and weights. Long distance runners can be very different in weight than athletes involved in weight lifting, discus and shot put. We don't know the individual sports that these athletes belonged to. Perhaps a better comparison would have been made if athletes were sampled from one sport, such as runners with runners, weight lifters with weight lifters etc.
However, I believe from the results of this investigation show that Australian male athletes tend to be heavier than female athletes back in the Australian athlete population. This makes sense as other studies I have carried out show that males also tend to be taller than females in the population.